Quantum physics has long established that nature places fundamental constraints on what can be known about the physical universe. Werner Heisenberg’s legendary uncertainty principle dictates that certain paired properties of particles, such as position and momentum, cannot both be measured simultaneously with unlimited precision. Crucially, this limitation is not the result of imperfect laboratory equipment or clumsy scientific instruments; rather, it is hardwired directly into the fundamental laws of nature.
However, position and time have historically occupied a different category in quantum mechanics, as Heisenberg’s original uncertainty principle does not impose the exact same restriction on these two quantities. Now, an international team of researchers has experimentally demonstrated another profound and fundamental limitation of nature: an electron’s precise location and its exact behavior over time cannot both be determined with arbitrary precision either.
Referred to as the "space-time limit," this newly observed physical relationship could carry major implications for the future development of quantum technologies, advanced computing, and ultrafast electronics.
The breakthrough discovery is the culmination of a large-scale international collaboration. It brings together leading research groups at the Regensburg Center for Ultrafast Nanoscopy (RUN)—led by Professors Jascha Repp, Rupert Huber, Franz Giessibl, and Klaus Richter—alongside an advanced theoretical team at the Max Planck Institute in Hamburg, headed by Angel Rubio.
Watching Electrons Move at Incredible Speeds
Comprehending how matter behaves at the absolute smallest scales of the universe is essential for engineering the next generation of technological infrastructure. Future advances in clean energy capture, high-capacity quantum computing, and powerful microelectronics designed to support artificial intelligence all rely heavily on understanding how chemical reactions unfold at a molecular level, how light dynamically interacts with novel materials, and how individual electrons travel through complex electronic circuits.
Yet, even the sharpest, highest-resolution microscopic photographs are incapable of revealing the complete picture. To fully grasp these microscopic phenomena, scientists must also be able to observe how these physical processes change continuously over time, effectively shooting high-definition, slow-motion movies of events occurring at the atomic scale.
At the Regensburg Center for Ultrafast Nanoscopy, researchers have been dedicated to developing advanced ultrafast microscopes capable of recording the movements of electrons, atoms, and molecules with extraordinary precision across both space and time. Approximately a decade ago, scientists in Regensburg successfully utilized ultrafast scanning tunneling microscopy to resolve the motion of a single molecule across both space and time for the very first time.
However, tracking individual electrons presents an exponentially greater experimental challenge. At these microscopic distances, electrons can move roughly a thousand times faster than heavier atoms and molecules, with critical physical changes taking place over durations measured merely in attoseconds.
To appreciate just how extreme these physical scales truly are, consider that an individual atom is approximately ten million times smaller than a single millimeter. Meanwhile, an attosecond is an almost unfathomable fraction of time: one-billionth of a billionth of a second. To put that into perspective, the difference between a single attosecond and one regular second is comparable to the difference between a single second and the entire age of the universe.
Making precise measurements under these conditions is exceptionally difficult because electrons do not behave like ordinary macroscopic objects. Instead of obeying the familiar, intuitive rules of classical physics, their motion is governed entirely by the unusual and counterintuitive laws of quantum mechanics.
Ultrafast Lasers Reveal Quantum Tunneling
To observe electron behavior at these extraordinary speeds, the research team constructed an entirely new laser system designed to provide much finer time resolution than any previously achieved in earlier experiments. This specialized system gives scientists the capability to directly control and study the quantum motion of individual electrons in real time.
During the experiments, carefully timed laser pulses drive electrons outward from an extremely sharp metal tip toward a silver surface. The actual physical distance the electrons travel across this gap is minute, spanning only a few atomic diameters.
The researchers detect this fleeting movement by measuring the resulting electrical current. To determine precisely when the electrons initiate their movement, the team deploys two distinct pulses of light separated by a meticulously controlled time interval.
Simon Maier, the lead author of the research paper, elaborates on the mechanism: "By varying the time interval between the two laser pulses, we can directly observe how the electrons respond."
This sophisticated approach yielded clear, undeniable evidence of electron motion occurring reliably on attosecond timescales. It demonstrated that the tailored laser pulses could successfully transfer electrons within these incredibly brief intervals while simultaneously allowing the scientists to observe the entire dynamic process as it unfolded.
What makes the final experimental result particularly remarkable is the specific manner in which the electrons travel across the gap. Rather than moving like conventional, solid particles, they behave as quantum waves. This wave-like nature enables them to pass directly through an energy barrier separating the metal tip from the silver surface, even though classical physics predicts they should utterly lack the energy required to cross it.
This strange phenomenon, known widely as quantum tunneling, can be visualized somewhat like a macroscopic object passing cleanly through a solid wall without causing any structural damage or breaking the material.
"Our measurement can be understood as a high-speed camera for the electron wave packets, since you can see at what point in time the tunneling process takes place," explains Katharina Glöckl, a doctoral student and co-author of the published study.
A Surprising 500-Attosecond Delay
To achieve a deeper analytical understanding of their empirical measurements, researchers working alongside Professor Angel Rubio conducted sophisticated quantum simulations modeling the complex behavior of electrons operating near the newly defined space-time limit.
These advanced theoretical calculations closely reproduced the empirical findings while simultaneously uncovering another striking detail: the electrons did not respond to the external light field instantaneously. Instead, their physical motion lagged behind the light field by approximately 500 attoseconds.
At such extreme micro-scales, several fundamental and seemingly conflicting features of quantum physics become critically important all at once.
For instance, the researchers discovered that the laser pulses could not be described adequately by treating light purely as a continuous wave, nor could they be explained solely by treating light as discrete packets of energy known as photons. Instead, the observed effects consistently displayed characteristics of both descriptions simultaneously. This dual behavior proved entirely essential for successfully exploring electron dynamics operating this close to the space-time limit.
Furthermore, the team discovered that actively controlling electron motion over extremely short time intervals fundamentally alters how those electrons are distributed across space. Quantum mechanics describes these electrons mathematically using wave packets, which illustrate how their underlying wave properties extend outward across various physical locations.
The intricate mathematical relationship between the precise timing of electron motion and the spatial extent of these wave packets ultimately pointed toward the central physical limitation driving the discovery.
A Hidden Tradeoff Between Space and Time
Raffael Spachtholz, another co-author of the research, explains the core constraint: "The more precisely we want to pin down the electron’s position in time, the more energy we need to provide. And as a result, the electron wave packet spreads out more spatially."
In practical terms, improving the precision of an electron’s timing comes with an unavoidable physical cost. The more tightly researchers define the exact moment when its motion occurs, the more broadly its associated quantum wave packet spreads out through physical space.
To test and examine this relationship experimentally, the team placed a single isolated atom directly onto the surface to effectively confine the electron wave packets to an extremely small, localized region immediately before the arrival of the laser pulses.
This specialized experimental setup enabled the scientists to directly measure the tight connection linking the spatial distribution of the electrons to the exact timing of their motion.
Crucially, even when the electrons absorbed substantial amounts of energy from the laser pulses, their resulting wave packets remained sufficiently localized to maintain high-resolution microscopy with both atomic spatial resolution and attosecond temporal resolution.
These new findings provide vital experimental insight into a fundamental space-time constraint that theoretical physicists had previously only suspected. They also open up practical pathways to systematically investigate how minute changes in electron motion over time directly impact the spatial structure of quantum wave functions.
Could Quantum Electronics Become Hundreds of Thousands of Times Faster?
Beyond revealing a previously hidden facet of fundamental quantum behavior, this discovery could eventually lay the groundwork for revolutionary technologies operating on timescales far beyond the outer limits of today’s advanced electronics.
One particularly promising application involves using precisely controlled electron wave packets to actively influence and direct chemical reactions.
Transferring a single electron to a molecule represents the absolute smallest possible transfer of electric charge in nature. However, when that single electron is concentrated tightly within an exceptionally small region of space and time, the resulting local peak current density can reach staggering levels—as high as 1 trillion amperes per square centimeter.
Under such extreme local conditions, scientists could gain entirely unprecedented methods for precisely controlling chemical bonds and observing in real time how complex molecules alter their structures during active chemical reactions.
"In the future, we want to use such wave packets to specifically trigger chemical reactions and observe, on the relevant length and time scales, how chemical bonds can be broken or altered," notes Prof. Jascha Repp.
The broader implications could extend well past the boundaries of chemistry. Achieving greater, more reliable control over electron motion may eventually help engineers design and build advanced electronic devices and quantum information processing systems that operate at speeds closely approaching the absolute fundamental limits of electron dynamics.
"In the long term, the insights gained could also contribute to operating electronics and quantum information processing at the intrinsic speed limit of electron motion itself—hundreds of thousands of times faster than the currently dominant CMOS technology," adds Prof. Rupert Huber.
Naturally, that ambitious scenario remains a long-term technological aspiration rather than an engineering milestone demonstrated in the current round of experiments. Nevertheless, the findings establish a robust new foundation for exploring how individual electrons can be manipulated at the smallest possible distances and the shortest possible timescales.
For Repp and Huber, the results strongly suggest that the range of potential future applications is extraordinarily broad. They remain convinced that future scientific advances in controlling electrons at the space-time limit will ultimately depend much more on human creativity and ingenuity than on the rigid constraints imposed by nature itself.
